Questions: Try Again Your answer is incorrect! The following data are the distances (in miles) for the 5 employees of a small business: 1, 9, 18, 4, 3 Send data to Excel Assuming that these distances constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places. (If necessary, consult a list of formulas.) X

Solution Steps

To find the mean (\( \mu \)) of the distances, we use the formula:

\[ \mu = \frac{\sum_{i=1}^N x_i}{N} \]

Substituting the values:

\[ \mu = \frac{1 + 9 + 18 + 4 + 3}{5} = \frac{35}{5} = 7.0 \]

Thus, the mean is \( 7.0 \).

The variance (\( \sigma^2 \)) is calculated using the formula:

\[ \sigma^2 = \frac{\sum (x_i - \mu)^2}{N} \]

Calculating the squared differences from the mean:

\[ (1 - 7)^2 = 36, \quad (9 - 7)^2 = 4, \quad (18 - 7)^2 = 121, \quad (4 - 7)^2 = 9, \quad (3 - 7)^2 = 16 \]

Summing these squared differences:

\[ \sum (x_i - \mu)^2 = 36 + 4 + 121 + 9 + 16 = 186 \]

Now, substituting into the variance formula:

\[ \sigma^2 = \frac{186}{5} = 37.2 \]

Thus, the variance is \( 37.2 \).

The standard deviation (\( \sigma \)) is the square root of the variance:

\[ \sigma = \sqrt{37.2} \approx 6.1 \]

Thus, the standard deviation is \( 6.1 \).

Final Answer